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function [fv,p,mx,Cx,Cy,b]=CWM(y,x,Nc,iter,optim,Sigmax)
% Fit mixture of linear regressors
Dy=size(y,1); % Dimension de y
Nf=size(x,1); % Dimension de x
Nt=size(x,2); % Cantidad de datos
f1=figure;
Lk=0;
Lopt=10^100;
for opt=1:optim
p=ones(Nc,1)/Nc; % p(Ci)
gx=zeros(Nt,1);
h=zeros(Nt,Nc);
b=zeros(Dy,Nf+1,Nc);
sigmay=cov(y');
sigmax=cov(x');
max(sigmax(:))
MAXy=max(y(1,:)); MINy=min(y(1,:));
mc=linspace(MINy,MAXy,Nc);
b(1,1,:)=mc+0*(rand(size(mc))-.5)*(MAXy-MINy)/Nc/2;
%for i=1:Nc
% [m,n]=min(abs(y(1,:)-mc(i)));
%end
k=fix(rand(1,Nc)*Nt)+1;
%cx=mean(x,2);
for i=1:Nc
mx(:,i)=x(:,k(i));
b(:,1,i)=y(:,k(i));
Cx(:,:,i)=.5*diag(diag(sigmax))/Nc^(1/Nf)+.5*eye(Nf,Nf)*max(sigmax(:))/Nc;
Cy(:,:,i)=1*sigmay/Nc;
end
% E STEP:
ss=0;
%%%%%% Calulo de P(Cj|y,x) -> h
for j=1:Nc
% Calculo de P(x,y|Cj)=P(y|x,Cj)*P(x|Cj)
% P(x|Cj):
xmx=x-repmat(mx(:,j),1,Nt);
iXa=inv(Cx(:,:,j));
xmX=iXa'*xmx;
dxm=sum(xmX.*xmx)';
% P(y|x,Cj):
ym=y-b(:,:,j)*[ones(1,Nt); xmx];
if Dy>1
iXa=inv(Cy(:,:,j));
ymY=ym'*iXa;
dym=dot(ymY',ym)';
else
dym=ym'.^2/Cy(:,:,j);
end
gxy=exp(-0.5*(dym+dxm))/sqrt(det(Cy(:,:,j)))/(2*pi)^(Dy/2)/sqrt(det(Cx(:,:,j)))/(2*pi)^(Nf/2);
gx(:,j)=exp(-0.5*(dxm))/sqrt(det(Cx(:,:,j)))/(2*pi)^(Nf/2);
% P(y,x):
h(:,j)=real(p(j)*gxy);
ss=ss+h(:,j);
end
% E-M algorithm
for k=1:iter
% visualization
disp(k)
figure(f1)
subplot(121)
cla
plot(x(1,:),x(2,:),'y.')
hold on
plot(mx(1,:),mx(2,:),'+')
axis('square')
axis([min(x(1,:)) max(x(1,:)) min(x(2,:)) max(x(2,:))])
drawnow
subplot(122)
cla
hold on
my=b(:,1,:);
plot(my(1,:),mx(1,:),'+')
axis('square')
title('output')
axis([min(y(1,:)) max(y(1,:)) min(x(1,:)) max(x(1,:))])
drawnow
for j=1:Nc
h(:,j)=h(:,j)./ss;
end
tic
% E
ss=0;
SUMtot=sum(h(:));
shj=sum(h);
Cxm=0;
for j=1:Nc
sh=shj(j);
p(j)=sh/SUMtot;
Cxm=Cxm+Cx(:,:,j)*p(j);
end
for j=1:Nc
% M-STEP
sh=shj(j);
p(j)=sh/SUMtot;
hDy=repmat(h(:,j)',Dy,1);
hNf=repmat(h(:,j)',Nf,1);
mx(:,j)=sum(hNf.*x,2)/sh;
my=sum(hDy.*y,2)/sh;
xmx=x-repmat(mx(:,j),1,Nt);
xmxp=xmx';
X=(hNf.*xmx)*xmxp/sh;
Cx(:,:,j)=X+Sigmax*eye(Nf,Nf)/Nc^(1/Nf)*mean(diag(sigmax));
iXa=pinv(Cx(:,:,j));
% Calculo de b
Bm=zeros(Nf+1,Nf+1); Bm(1,1)=1;
Bm(2:Nf+1,2:Nf+1)=iXa;
yxm=(hDy.*y)*xmxp/sh;
Am=[my yxm];
b(:,:,j)=Am*Bm';
%calculo de Cy
ym=y-b(:,:,j)*[ones(1,Nt); xmx];
if Dy>1
Cy(:,:,j)=(hDy.*ym)*ym'/sh+0.4*diag([10000/1 100/6].^2);
else
Cy(:,:,j)=(hDy.*ym)*ym'/sh+.1;
end
% STAGE E:
iXa=pinv(Cxm);
xmX=iXa'*xmx;
dxm=sum(xmX.*xmx);
% P(y|x,Cj):
if Dy>1
iXa=inv(Cy(:,:,j));
ymY=iXa'*ym;
dym=dot(ymY,ym);
else
dym=ym.*ym/Cy(:,:,j);
end
%gxy=exp(-0.5*(dym+dxm))/sqrt(det(Cy(:,:,j)))/(2*pi)^(Dy/2+Nf/2)*sqrt(det(iXa))/(2*pi)^(Nf/2);
%size(gxy)
% gx(:,j)=exp(-0.5*(dxm'))*sqrt(det(iXa))/(2*pi)^(Nf/2);
% P(y,x):
h(:,j)=p(j)*(exp(-0.5*dym)/sqrt(det(Cy(:,:,j)))/(2*pi)^(Dy/2)).*exp(-0.5*(dxm))*sqrt(det(iXa))/(2*pi)^(Nf/2);
ss=ss+h(:,j);
end
toc
L=-sum(log(ss));
Lk(k,opt)=L;
end
p_opt=p;
mx_opt=mx;
Cx_opt=Cx;
Cy_opt=Cy;
b_opt=b;
Lopt=L;
end
p=p_opt;
mx=mx_opt;
Cx=Cx_opt;
Cy=Cy_opt;
b=b_opt;
fv=Lopt;
close
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